Linear classifiers with random convolution kernels are computationally efficient methods that need no design or domain knowledge. Unlike deep neural networks, there is no need to hand-craft a network architecture; the kernels are randomly generated and only the linear classifier needs training. A recently proposed method, RandOm Convolutional KErnel Transforms (ROCKETs), has shown high accuracy across a range of time-series data sets. Here we propose a multi-scale version of this method, using both high- and low-frequency components. We apply our methods to inter-burst detection in a cohort of preterm EEG recorded from 36 neonates <30 weeks gestational age. Two features from the convolution of 10,000 random kernels are combined using ridge regression. The proposed multi-scale ROCKET method out-performs the method without scale: median (interquartile range, IQR) Matthews correlation coefficient (MCC) of 0.859 (0.815 to 0.874) for multi-scale versus 0.841 (0.807 to 0.865) without scale, p<0.001. The proposed method lags behind an existing feature-based machine learning method developed with deep domain knowledge, but is fast to train and can quickly set an initial baseline threshold of performance for generic and biomedical time-series classification.